Statistical Mechanics - Physics at Oregon State University
Statistical Mechanics - Physics at Oregon State University
Statistical Mechanics - Physics at Oregon State University
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IV CONTENTS<br />
4.3 Gas of poly-<strong>at</strong>omic molecules. . . . . . . . . . . . . . . . . . . . . 77<br />
4.4 Degener<strong>at</strong>e gas. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79<br />
4.5 Fermi gas. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80<br />
4.6 Boson gas. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85<br />
4.7 Problems for chapter 4 . . . . . . . . . . . . . . . . . . . . . . . . 87<br />
5 Fermions and Bosons 89<br />
5.1 Fermions in a box. . . . . . . . . . . . . . . . . . . . . . . . . . . 89<br />
5.2 Bosons in a box. . . . . . . . . . . . . . . . . . . . . . . . . . . . 106<br />
5.3 Bose-Einstein condens<strong>at</strong>ion. . . . . . . . . . . . . . . . . . . . . . 113<br />
5.4 Problems for chapter 5 . . . . . . . . . . . . . . . . . . . . . . . . 115<br />
6 Density m<strong>at</strong>rix formalism. 119<br />
6.1 Density oper<strong>at</strong>ors. . . . . . . . . . . . . . . . . . . . . . . . . . . 119<br />
6.2 General ensembles. . . . . . . . . . . . . . . . . . . . . . . . . . . 123<br />
6.3 Maximum entropy principle. . . . . . . . . . . . . . . . . . . . . . 125<br />
6.4 Equivalence of entropy definitions for canonical ensemble. . . . . 134<br />
6.5 Problems for chapter 6 . . . . . . . . . . . . . . . . . . . . . . . . 136<br />
7 Classical st<strong>at</strong>istical mechanics. 139<br />
7.1 Rel<strong>at</strong>ion between quantum and classical mechanics. . . . . . . . . 139<br />
7.2 Classical formul<strong>at</strong>ion of st<strong>at</strong>istical mechanical properties. . . . . 142<br />
7.3 Ergodic theorem. . . . . . . . . . . . . . . . . . . . . . . . . . . . 144<br />
7.4 Wh<strong>at</strong> is chaos? . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146<br />
7.5 Ideal gas in classical st<strong>at</strong>istical mechanics. . . . . . . . . . . . . . 149<br />
7.6 Normal systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . 151<br />
7.7 Quadr<strong>at</strong>ic variables. . . . . . . . . . . . . . . . . . . . . . . . . . 151<br />
7.8 Effects of the potential energy. . . . . . . . . . . . . . . . . . . . 152<br />
7.9 Problems for chapter 7 . . . . . . . . . . . . . . . . . . . . . . . . 154<br />
8 Mean Field Theory: critical temper<strong>at</strong>ure. 157<br />
8.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157<br />
8.2 Basic Mean Field theory. . . . . . . . . . . . . . . . . . . . . . . . 161<br />
8.3 Mean Field results. . . . . . . . . . . . . . . . . . . . . . . . . . . 164<br />
8.4 Density-m<strong>at</strong>rix approach (Bragg-Williams approxim<strong>at</strong>ion. . . . . 168<br />
8.5 Critical temper<strong>at</strong>ure in different dimensions. . . . . . . . . . . . . 177<br />
8.6 Bethe approxim<strong>at</strong>ion. . . . . . . . . . . . . . . . . . . . . . . . . 181<br />
8.7 Problems for chapter 8 . . . . . . . . . . . . . . . . . . . . . . . . 188<br />
9 General methods: critical exponents. 191<br />
9.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191<br />
9.2 Integr<strong>at</strong>ion over the coupling constant. . . . . . . . . . . . . . . . 192<br />
9.3 Critical exponents. . . . . . . . . . . . . . . . . . . . . . . . . . . 197<br />
9.4 Rel<strong>at</strong>ion between susceptibility and fluctu<strong>at</strong>ions. . . . . . . . . . 203<br />
9.5 Exact solution for the Ising chain. . . . . . . . . . . . . . . . . . 205<br />
9.6 Spin-correl<strong>at</strong>ion function for the Ising chain. . . . . . . . . . . . . 210